2007 iTest Problems/Problem 7
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Problem
An equilateral triangle with side length 
has the same area as a square with side length 
.
Find .
![\mathrm{(A)}\,\frac{\sqrt[4]{3}}{2}\quad\mathrm{(B)}\,\frac{\sqrt[4]{3}}{\sqrt{2}}\quad\mathrm{(C)}\,1\quad\mathrm{(D)}\,\fra...](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/4/e/7/4e7bddbc56b423660bb2f7d3ac97619400f2d1cf.gif)
Solution
An equilateral triangle with side length 1 has an area of 
, and a square with that area has a side length of ![\sqrt{\frac{\sqrt{3}}{4}}=\frac{\sqrt[4]{3}}{2} \Rightarrow \mathrm{(A)}](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/4/7/c/47c3b0d68ac21d1e2c267cd4ec789c9f6dc30226.gif)
See Also
| 2007 iTest (Problems) | ||
| Preceded by: Problem 6 | Followed by: Problem 8 | |
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